Harmonic projection and hypercentral extensions
Group Theory
2026-02-03 v1
Abstract
The Liouville property is a strong form of amenability, but contrary to amenability, it is not well-behaved under extensions. In this paper it is shown that, for some measures, the Liouville property is preserved by [FC-]hypercentral extensions. To this end a projection from onto the space of harmonic functions is introduced.
Cite
@article{arxiv.2602.00187,
title = {Harmonic projection and hypercentral extensions},
author = {Antoine Gournay},
journal= {arXiv preprint arXiv:2602.00187},
year = {2026}
}
Comments
12 pages